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Abstract:
We consider the EPRL spin foam amplitude for arbitrary embedded
two-complexes. Choosing a definition of the face- and edge amplitudes which
lead to spin foam amplitudes invariant under trivial subdivisions, we
investigate invariance properties of the amplitude under consistent
deformations, which are deformations of the embedded two-complex where faces
are allowed to pass through each other in a controlled way. Using this
surprising invariance, we are able to show that in the physical Hilbert space
as defined by the sum over all spin foams contains no knotting classes of
graphs anymore.